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Chapter 13: Q.13.33 (page 542)
We stated earlier that a one-way ANOVA test is always right-tailed because the null hypothesis is rejected only when the test statistic, , is too large. Why is the null hypothesis rejected only when is too large?
Rejection of the null hypothesis.
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Breast Milk and IQ. Considerable controversy exists over whether long-term neurodevelopment is affected by nutritional factors in early life. A. Lucas and R. Morley summarized their findings on that question for preterm babies in the publication "Breast Milk and Subsequent Intelligence Quotient in Children Born Preterm (The Lancet, Vol. 339, Issue 8788, Pp, 261-264). The researchers analyzed IQ data on children at age years. The mothers of the children in the study had chosen whether to provide their infants with breast milk within hours of delivery. The researchers used the following designations. Group I: mothers declined to provide breast milk; Group ll a: mothers had chosen but were unable to provide breast milk and Group Il b; mothers had chosen and were able to provide breast milk. Here are the summary statistics on IQ.
At the significance level, do the data provide sufficient evidence to conclude that a difference exists in mean IQ at age years for preterm children among the three groups? Note: For the degrees of freedom in this exercise:
Show that, for two populations, , where is the pooled variance defined in Section 10.2 on page 407 . Conclude that is the pooled sample standard deviation, .
Artificial Teeth: Wear. In a study by J. Zeng et al. three materials for making artificial teeth-Endura, Duradent, and Duracross-were tested for wear. Their results were published as the paper "In Vitro Wear Resistance of Three Types of Composite Resin Denture Teeth" (Journal of Prosthetic Dentistry, Vol. 94 . Issue 5. pp. 453-457 ). Using a machine that simulated grinding by two right first molars at 60 strokes per minute for a total of 50,000 strokes, the researchers measured the volume of material worn away, in cubic millimeters. Six pairs of teeth were tested for each material. The data on the WeissStats site are based on the results obtained by the researchers. At the 5 % significance level, do the data provide sufficient evidence to conclude that there is a difference in mean wear among the three materials?
We have provided data from independent simple random samples from several populations. In each case, determine the following items.
a. SSTR
b. MSTR
c. SSE
d. MSE
e. F
| Sample 1 | Sample 2 | Sample 3 |
| 5 | ||
For a one-way ANOVA test, suppose that, in reality, the null hypothesis is false. Does that mean that no two of the populations have the same mean? If not, what does it mean?
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